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      SUBROUTINE <a name="CGTTS2.1"></a><a href="cgtts2.f.html#CGTTS2.1">CGTTS2</a>( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      INTEGER            ITRANS, LDB, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * )
      COMPLEX            B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CGTTS2.18"></a><a href="cgtts2.f.html#CGTTS2.1">CGTTS2</a> solves one of the systems of equations
</span><span class="comment">*</span><span class="comment">     A * X = B,  A**T * X = B,  or  A**H * X = B,
</span><span class="comment">*</span><span class="comment">  with a tridiagonal matrix A using the LU factorization computed
</span><span class="comment">*</span><span class="comment">  by <a name="CGTTRF.21"></a><a href="cgttrf.f.html#CGTTRF.1">CGTTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ITRANS  (input) INTEGER
</span><span class="comment">*</span><span class="comment">          Specifies the form of the system of equations.
</span><span class="comment">*</span><span class="comment">          = 0:  A * X = B     (No transpose)
</span><span class="comment">*</span><span class="comment">          = 1:  A**T * X = B  (Transpose)
</span><span class="comment">*</span><span class="comment">          = 2:  A**H * X = B  (Conjugate transpose)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NRHS    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of right hand sides, i.e., the number of columns
</span><span class="comment">*</span><span class="comment">          of the matrix B.  NRHS &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DL      (input) COMPLEX array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The (n-1) multipliers that define the matrix L from the
</span><span class="comment">*</span><span class="comment">          LU factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The n diagonal elements of the upper triangular matrix U from
</span><span class="comment">*</span><span class="comment">          the LU factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DU      (input) COMPLEX array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The (n-1) elements of the first super-diagonal of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DU2     (input) COMPLEX array, dimension (N-2)
</span><span class="comment">*</span><span class="comment">          The (n-2) elements of the second super-diagonal of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IPIV    (input) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The pivot indices; for 1 &lt;= i &lt;= n, row i of the matrix was
</span><span class="comment">*</span><span class="comment">          interchanged with row IPIV(i).  IPIV(i) will always be either
</span><span class="comment">*</span><span class="comment">          i or i+1; IPIV(i) = i indicates a row interchange was not
</span><span class="comment">*</span><span class="comment">          required.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the matrix of right hand side vectors B.
</span><span class="comment">*</span><span class="comment">          On exit, B is overwritten by the solution vectors X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B.  LDB &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, J
      COMPLEX            TEMP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          CONJG
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 .OR. NRHS.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      IF( ITRANS.EQ.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve A*X = B using the LU factorization of A,
</span><span class="comment">*</span><span class="comment">        overwriting each right hand side vector with its solution.
</span><span class="comment">*</span><span class="comment">
</span>         IF( NRHS.LE.1 ) THEN
            J = 1
   10       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L*x = b.
</span><span class="comment">*</span><span class="comment">
</span>            DO 20 I = 1, N - 1
               IF( IPIV( I ).EQ.I ) THEN
                  B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
               ELSE
                  TEMP = B( I, J )
                  B( I, J ) = B( I+1, J )
                  B( I+1, J ) = TEMP - DL( I )*B( I, J )
               END IF
   20       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U*x = b.
</span><span class="comment">*</span><span class="comment">
</span>            B( N, J ) = B( N, J ) / D( N )
            IF( N.GT.1 )
     $         B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
     $                       D( N-1 )
            DO 30 I = N - 2, 1, -1
               B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
     $                     B( I+2, J ) ) / D( I )
   30       CONTINUE
            IF( J.LT.NRHS ) THEN
               J = J + 1
               GO TO 10
            END IF
         ELSE
            DO 60 J = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L*x = b.
</span><span class="comment">*</span><span class="comment">
</span>               DO 40 I = 1, N - 1
                  IF( IPIV( I ).EQ.I ) THEN
                     B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
                  ELSE
                     TEMP = B( I, J )
                     B( I, J ) = B( I+1, J )
                     B( I+1, J ) = TEMP - DL( I )*B( I, J )
                  END IF
   40          CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U*x = b.
</span><span class="comment">*</span><span class="comment">
</span>               B( N, J ) = B( N, J ) / D( N )
               IF( N.GT.1 )
     $            B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
     $                          D( N-1 )
               DO 50 I = N - 2, 1, -1
                  B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
     $                        B( I+2, J ) ) / D( I )
   50          CONTINUE
   60       CONTINUE
         END IF
      ELSE IF( ITRANS.EQ.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve A**T * X = B.
</span><span class="comment">*</span><span class="comment">
</span>         IF( NRHS.LE.1 ) THEN
            J = 1
   70       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U**T * x = b.
</span><span class="comment">*</span><span class="comment">
</span>            B( 1, J ) = B( 1, J ) / D( 1 )
            IF( N.GT.1 )
     $         B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
            DO 80 I = 3, N
               B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
     $                     B( I-2, J ) ) / D( I )
   80       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L**T * x = b.
</span><span class="comment">*</span><span class="comment">
</span>            DO 90 I = N - 1, 1, -1
               IF( IPIV( I ).EQ.I ) THEN
                  B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
               ELSE
                  TEMP = B( I+1, J )
                  B( I+1, J ) = B( I, J ) - DL( I )*TEMP
                  B( I, J ) = TEMP
               END IF
   90       CONTINUE
            IF( J.LT.NRHS ) THEN
               J = J + 1
               GO TO 70
            END IF
         ELSE
            DO 120 J = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U**T * x = b.
</span><span class="comment">*</span><span class="comment">
</span>               B( 1, J ) = B( 1, J ) / D( 1 )
               IF( N.GT.1 )
     $            B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
               DO 100 I = 3, N
                  B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
     $                        DU2( I-2 )*B( I-2, J ) ) / D( I )
  100          CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L**T * x = b.
</span><span class="comment">*</span><span class="comment">
</span>               DO 110 I = N - 1, 1, -1
                  IF( IPIV( I ).EQ.I ) THEN
                     B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
                  ELSE
                     TEMP = B( I+1, J )
                     B( I+1, J ) = B( I, J ) - DL( I )*TEMP
                     B( I, J ) = TEMP
                  END IF
  110          CONTINUE
  120       CONTINUE
         END IF
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve A**H * X = B.
</span><span class="comment">*</span><span class="comment">
</span>         IF( NRHS.LE.1 ) THEN
            J = 1
  130       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U**H * x = b.
</span><span class="comment">*</span><span class="comment">
</span>            B( 1, J ) = B( 1, J ) / CONJG( D( 1 ) )
            IF( N.GT.1 )
     $         B( 2, J ) = ( B( 2, J )-CONJG( DU( 1 ) )*B( 1, J ) ) /
     $                     CONJG( D( 2 ) )
            DO 140 I = 3, N
               B( I, J ) = ( B( I, J )-CONJG( DU( I-1 ) )*B( I-1, J )-
     $                     CONJG( DU2( I-2 ) )*B( I-2, J ) ) /
     $                     CONJG( D( I ) )
  140       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L**H * x = b.
</span><span class="comment">*</span><span class="comment">
</span>            DO 150 I = N - 1, 1, -1
               IF( IPIV( I ).EQ.I ) THEN
                  B( I, J ) = B( I, J ) - CONJG( DL( I ) )*B( I+1, J )
               ELSE
                  TEMP = B( I+1, J )
                  B( I+1, J ) = B( I, J ) - CONJG( DL( I ) )*TEMP
                  B( I, J ) = TEMP
               END IF
  150       CONTINUE
            IF( J.LT.NRHS ) THEN
               J = J + 1
               GO TO 130
            END IF
         ELSE
            DO 180 J = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U**H * x = b.
</span><span class="comment">*</span><span class="comment">
</span>               B( 1, J ) = B( 1, J ) / CONJG( D( 1 ) )
               IF( N.GT.1 )
     $            B( 2, J ) = ( B( 2, J )-CONJG( DU( 1 ) )*B( 1, J ) ) /
     $                        CONJG( D( 2 ) )
               DO 160 I = 3, N
                  B( I, J ) = ( B( I, J )-CONJG( DU( I-1 ) )*
     $                        B( I-1, J )-CONJG( DU2( I-2 ) )*
     $                        B( I-2, J ) ) / CONJG( D( I ) )
  160          CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L**H * x = b.
</span><span class="comment">*</span><span class="comment">
</span>               DO 170 I = N - 1, 1, -1
                  IF( IPIV( I ).EQ.I ) THEN
                     B( I, J ) = B( I, J ) - CONJG( DL( I ) )*
     $                           B( I+1, J )
                  ELSE
                     TEMP = B( I+1, J )
                     B( I+1, J ) = B( I, J ) - CONJG( DL( I ) )*TEMP
                     B( I, J ) = TEMP
                  END IF
  170          CONTINUE
  180       CONTINUE
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CGTTS2.269"></a><a href="cgtts2.f.html#CGTTS2.1">CGTTS2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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